methods (well-defined procedures, recipes) for construction are called
algorithms

there is an algorithm for constructing an Euler circuit: Fleury's
algorithm

we will illustrate it with the graph:

Fleury's
Algorithm

1. pick any vertex to start
2. from that vertex pick an edge to traverse (see below for important
rule)
3. darken that edge, as a reminder that you can't traverse it
again
4. travel that edge, coming to the next vertex
5. repeat 2-4 until all edges have been traversed, and you are
back at the starting vertex